Solve for $x$ and $y$ using elimination. ${-6x+6y = -24}$ ${-5x-5y = -60}$
Explanation: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-6$ ${-30x+30y = -120}$ $30x+30y = 360$ Add the top and bottom equations together. $60y = 240$ $\dfrac{60y}{{60}} = \dfrac{240}{{60}}$ ${y = 4}$ Now that you know ${y = 4}$ , plug it back into $\thinspace {-6x+6y = -24}\thinspace$ to find $x$ ${-6x + 6}{(4)}{= -24}$ $-6x+24 = -24$ $-6x+24{-24} = -24{-24}$ $-6x = -48$ $\dfrac{-6x}{{-6}} = \dfrac{-48}{{-6}}$ ${x = 8}$ You can also plug ${y = 4}$ into $\thinspace {-5x-5y = -60}\thinspace$ and get the same answer for $x$ : ${-5x - 5}{(4)}{= -60}$ ${x = 8}$